What is the reason some no longer pronounce the letter "T" at the end of some words?

Over the last year or so, I have noticed that many on Sports Talk Radio no longer pronounce the "T" sound at the end of some words. "Last year " has become "lass year." "Next year" is pronounced "nex' year." "Draft" is now "draf'." (As I was typing this, the NFL Commissioner just did it!!!)
It started with athletes and ex-athletes. It expanded to talk show hosts. (Mike Gohlic, Colin Cowherd. Even Paul Finebaum and Dan Patrick.) Now, even the people doing promotional ads are doing it!
These are educated people! Why do they do this? Are they trying to be "cool"? It makes them sound like a bunch of illiterates!!!